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Rigidity of convex
divisible domains in flag manifolds
Wouter Van Limbeek and Andrew Zimmer |
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Geometry & Topology 23 (2019) 171–240
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Abstract |
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In contrast to the many examples of convex divisible domains in real projective space, we prove that up to projective isomorphism there is only one convex divisible domain in the Grassmannian of –planes in when . Moreover, this convex divisible domain is a model of the symmetric space associated to the simple Lie group . |
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Keywords
flag manifolds, geometric structures, convex divisible
domains, Hilbert metric, rigidity, Grassmannian
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Mathematical Subject Classification 2010
Primary: 53C24, 57N16
Secondary: 22E40, 22F50, 52A20, 57S30
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References |
Publication
Received: 16 May 2017
Accepted: 21 July 2018
Published: 5 March 2019
Proposed: Anna Wienhard
Seconded: Bruce Kleiner, Benson Farb
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Authors |
| Wouter Van Limbeek | |
| Department of Mathematics,
Statistics, and Computer Science University of Illinois at Chicago Chicago, IL United States |
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| Andrew Zimmer | |
| Department of Mathematics Louisiana State University Baton Rouge, LA United States |
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